Experimental Log: Roger Bland, December 30-31, 2001
Starting to Look for RAFOS Signals
( logbook | ifremer on RAFOS |Garfield at NPS )

8H38 Sunday December 30, 2001. I am ready to start signal compression on the beam-formed, band-width-limited 2-hour signal files (e.g.: r0124506.27w -> r0124506.27d using rafdet.pro).

But first, I need to make some cross checks to understand the data. (And maybe some day I should actually do a detailed numerical verification - later.) I will investigate signal sizes for this data, the first run with a RAFOS signal.

Here is a 2-hour beam-formed signal. The rms can be estimated from Horowitz's rule of thumb, that the rms is about equal to 1/8 of the peak-to-peak "envelope." I estimate this to give rms = 1/8 * 3000 = 400. An exact calculation gives 382.593 for the full 7,376,896 - point time series.

filesampling rate
(Hz)
rms
r0124506.27b1000382.6
r0124506.27w7.81217.56

Here is the same data, mixed with 260 Hz and downsampled by averaging 128 points together. From the graph, the rms should come out to be 120 * 1/8 = 15. Exact calculation gives 17.56 for the full 57,632 - point time series.

I have realized that mixing with a sine wave of amplitude 1 results in reducing the size of a signal by a factor of 1/2, as well as shifting the frequency. So, taking this into account, we can predict the rms of the .w file from that of the .b file. I will assume that the power spectrum is flat, and that the bandwidth of both signals is proportional to the sampling rate. Then

```	rmsw-pred = rmsb-obs * (BWw/BWb)1/2 *(1/2)
=382.6 * (1/128)1/2 * (1/2)
= 16.9
```
The agreement is so good as to be fortuituous (no reason for the power spectrum to be flat).

16H01. Note the features in the narrow-band data, in order of maximum amplitude on the graph above:

Large signals after narrow-band filtering, r0124506.27
time (sec)amplitude
(.w file)
amplitude
(.d file)
2405530
987265
6378230
2791-182
3170-160
600152
5000130
Blowups of the larger of these peaks show that they are narrow disturbances, not RAFOS signals.

18:48 Monday December 31, 2001. Still a little time left before New Year's Eve starts.

I have just realized that the file I am working on starts at 6:27 Zulu and so is not expected to have any RAFOS signals. I was chagrined at not being able to see them. Now I feel a little better. I will try to hone up my detection scheme on this null file, then try it on some others.

I am pretty sure that the raw (but beam-formed) signal (r0124506.27b) will not show the RAFOS signals. Their power level is below the integrated power from zero to 400 Hz. However, I think that the band-pass signal should show it. I am a little unclear on its bandwidth, and even less clear on the degree of aliasing admitted by the procedure of combining points. However, as a first guess I would say that the bandwidth is twice the Nyquist frequency, or about 8 Hz - I am not clear about negative frequencies. At any rate, I think that the RAFOS signal should be visible in this frequency band.

A way to make the signal stand out more would be to square and average over 80 seconds. This should be pretty easy. I will try it . . . here is the result. The general level of the averaged squared signal, around 350, corresponds quite well to the square of the rms given in the table above. (Just a consistency check.)

This might be the end of my research for the year 2001.

HAPPY NEW YEAR!